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Three coins are tossed once. Let $A$ denote the event "three heads shows". $B$ denote the event "two heads and one tail show", $C$ denote the event "three tails show" and $D$ denote the event "a head shows on the first coin". Which events are
(i) mutually exclusive?
(ii) sample ?
(iii) compound?
(i) mutually exclusive?
(ii) sample ?
(iii) compound?
Solution:
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Verified Answer
When three coins are tossed then the sample space $S$ is
$=\{$ HHH, HHT, HTH, HTT, THH, THT, TTH, TTT $\}$
$\therefore \quad A=$ Three heads show $=\{H H H\}$
$B$ : Two heads and one tail show
$=\{H H T, H T H, T H H\}$
$C:$ A three tails show $=\{T T T\}$
$D$ : A head show on the first coin,
$=\{H H H, H H T, H T H, H T T\}$
(i) Since $A \cap B=\phi, A \cap C=\phi$,
$B \cap C=\phi, C \cap D=\phi, A \cap B \cap C=\phi$
$\Rightarrow A$ and $B, A$ and $C, B$ and $C, C$ and $D$
(ii) $A$ and $C$ are simple events.
(iii) $B$ and $D$ are compound events.
$=\{$ HHH, HHT, HTH, HTT, THH, THT, TTH, TTT $\}$
$\therefore \quad A=$ Three heads show $=\{H H H\}$
$B$ : Two heads and one tail show
$=\{H H T, H T H, T H H\}$
$C:$ A three tails show $=\{T T T\}$
$D$ : A head show on the first coin,
$=\{H H H, H H T, H T H, H T T\}$
(i) Since $A \cap B=\phi, A \cap C=\phi$,
$B \cap C=\phi, C \cap D=\phi, A \cap B \cap C=\phi$
$\Rightarrow A$ and $B, A$ and $C, B$ and $C, C$ and $D$
(ii) $A$ and $C$ are simple events.
(iii) $B$ and $D$ are compound events.
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